Geostatistics, which can be defined as the tools for studying and predicting the spatial structure of georeferenced variables, have been mainly used in soil science during the past two decades. Since now, hundreds of geostatistical papers have been published on soil science issues. The use of geostatistical tools in soil science is diverse and extensive. It can be for studying and predicting soil contamination in industrial areas, for building agrochemical maps at the field level, or even to map physical and chemical soil properties for a global extent. The users of the output maps are going from soil scientists to environmental modelers. One of the specificity of geostatistical outputs is the assessment of the spatial accuracy associated to the spatial prediction of the targeted variable. The results which are quantitative are then associated to a level of confidence which is spatially variable. The spatial accuracy can then be integrated into environmental models, allowing for a quantitative assessment of soil scenarios.

Geostatistics are one of the most popular tools of pedometrics (the application of mathematical and statistical methods for the study of the distribution and genesis of soils), as well as digital soil mapping which is defined as the creation and the population of geographically referenced soil databases generated at a given spatial resolution by using field and laboratory observation methods coupled with environmental data through quantitative relationships. In pedometrics, geostatistics are then exploratory tool for understanding the distribution and the genesis of soil whereas in digital soil mapping they have mapping as finality. Geostatistics are also valuable supplement to classical soil mapping since they allow for recovering data knowledge hidden in traditional soil maps.

In this book, we call 'soil geography' the study of the spatial distribution of the soil cover which concerns physical, chemical and biological soil properties, their vertical and lateral variability (the spatial variability), and their description through the use of taxonomic tools. The spatial variation of soil properties can be defined as a function of three parameters: (1) the average value determined by the soil forming factors (the corpan factors or climate, organisms, relief, parent material, time and location), (2) its local variation (function of scale and extent), (3) the stochastic or pseudotochastic variation (Chapter 1). The geostatistics are then applied in this context. So that to illustrate the spatial variation factors and strength the advantages of using geostatistics, we can use the following example. Let say that the target issue is to map values of humus content of a specific area. The first spatial soil variation parameter can be determined by a certain amount of samples. The humus content values may vary regularly, e.g., along the slope or any other gradient of local factors. In most cases, this variation is not found at first glance, because the values increase or decrease irregularly; in other situations, the changes can be along a more complex surface. In that case, one should search for a trend, a regression dependence on the coordinates. Medium value and local trend constitute a deterministic component of soil variability. The second parameter of spatial variation does not depend on coordinates, but only on the distance between the sampling units (sampling resolution).

This component can be analysed with geostatistics. Finally, the third parameter of spatial soil variation is completely random, and practically cannot be interpreted; in geostatistical models, it is expressed by the 'nugget' - variability that does not depend either on coordinates or on the lag distance. These notions and concepts are further detailed by Webster (chapter 1 of this book).

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